Orbiting spacecraft are commonly stabilized by spinning them about their longitudinal axes. Any lateral perturbations, such as those produced by roll or yaw tip off torques that occur at booster separation or by energy dissipation due to sloshing of fuel within the fuel tanks, cause nutation motion to develop whereby the spacecraft tends to cone about the nominal spin axis. The nutation has a frequency generally corresponding to the spin rate and mass distribution of the spacecraft. A general discussion of nutation motion is given in Section 9-12 of Sears, Zemansky and Young, University Physics, Fifth Edition, Addison Wesley Publishing Company, 1977.
In general, nutation is a word commonly used to describe a coning motion of the nominal spin axis of a spinning body about a line fixed in space and determined by the inertial orientation of the angular momentum vector for the system. The inertial nutation frequency .psi. in radians per second is: EQU .psi.=H/A (1)
where
H=magnitude of the system angular momentum in ft-lb-sec, and PA1 A=system transverse moment of inertia in ft-lb-sec.sup.2 (with "transverse" implying normal to the nominal spin axis) PA1 C=system spin axis moment of inertia and PA1 .theta.=nutation angle (usually very small)
Active nutation damping is a process which reduces the magnitude of a nutation angle .theta. by the application of properly timed torque vector pulses to the body. These pulses are typically produced by the firing of hot or cold gas thrusters. If T is the applied torque vector, the response of the system is determined by the following differential equation: EQU (d/dt)H=T (2)
The timing of the pulses is selected in such a way that the angular momentum vector is moved toward the nominal spin axis with each firing, thus causing a nutation angle reduction. The period P of gas thruster pulsing is determined by: ##EQU1## where .sigma.=C/A=system moment of inertia ratio and
The phasing of the pulses is controlled relative to the output of the nutation sensor, e.g., a linear or angular accelerometer, on the spinning body. A typical nutation damping sequence consists of a series of consecutive, constant magnitude pulses which terminates when the amplitude of the sensor output is reduced to a magnitude below a predetermined threshold level.
In general, each torque pulse applied to the spinning body changes the inertial orientation of the angular momentum vector which in general represents an undesirable side effect. For a series of constant duration pulses, the inertial motion of the momentum vector is quasi-periodic. A typical momentum vector path viewed from a position above the initial angular momentum vector is in the form of an open or closed regular polygon. The net spin axis attitude disturbance produced by the series of pulses depends upon where the angular momentum vector is located after the last thruster firing. The size of the polygon is related to the moment of inertia ratio .sigma. and increases without limit as .sigma..fwdarw.1.
The nominal orientation of the spin stabilized spacecraft is critical because the craft must be oriented precisely among other reasons to ensure proper heading during thrusting to reposition the craft; it is thus necessary to minimize attitude disturbances which tend to occur as the nutation damping jets are fired during a nutation control sequence to return the craft to its near zero nutation condition.
It is possible to control within limits the attitude disturbances by controlling the number of constant duration pulses fired. In the constant duration firing pulse strategy of the prior art, the control strategy requires precise knowledge of the system moment of inertia ratio that is difficult to predict. Furthermore, some inertia ratios do not lend themselves to this approach.
It is accordingly an object of the present invention to provide a method of damping nutation motion in a spinning body that produce minimum attitude disturbances about the nominal spin axis of the spacecraft.
Another object is to provide a new and improved method of damping nutation motion in a spacecraft, wherein no knowledge of system moment of inertia ratio is required.
Another object is to provide a method of damping nutation motion in a spacecraft at high thruster usage efficiency.